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Transform-domain sample-by-sample decision feedback equalizerRelated Patent Categories: Pulse Or Digital Communications, Equalizers, Automatic, Adaptive, Decision Feedback EqualizerTransform-domain sample-by-sample decision feedback equalizer description/claimsThe Patent Description & Claims data below is from USPTO Patent Application 20060146925, Transform-domain sample-by-sample decision feedback equalizer. Brief Patent Description - Full Patent Description - Patent Application Claims
[0001] The present invention is directed to methods and apparatuses for processing received digital signals in a digital communications system, and more particularly to a method and apparatus for processing received digital signals in a digital communications system using packet based signals in the presence of noise and inter-symbol interference. [0002] Adaptive equalizers are often used in digital communication systems to mitigate inter-symbol interference caused by multi-path. Among the many variants of adaptive equalizers, Least Mean Squares (LMS) type decision feedback equalizers are the most frequently used. For emerging applications where the channel is dynamic or requiring fast convergence speed, the traditional LMS-type equalizers often exhibit inadequate performance. [0003] The convergence speed of traditional time-domain LMS type adaptive equalizers depends on the ratio of the maximum to the minimum eigenvalues of the autocorrelation matrix of the input. Filters having inputs with a wide eigenvalue spread often take longer to converge than filters with white noise inputs. [0004] As a remedy to this problem, transform domain equalizers were developed. These equalizers are based on orthogonalization of the input signals, which are often referred to as frequency-domain adaptive filters. Such orthogonalization techniques have been used in the context of linear (FIR) adaptive filters. Simulations have shown that such equalizers have better convergence properties compared to the counterpart time-domain LMS algorithms. Unfortunately, linear equalizers perform very poorly if the channel spectrum contains dip nulls or the inverse of the channel has strong samples outside the range of the linear equalizer. As a result, they suffer from noise-enhancement or lack adequate numbers of taps. Inter symbol interference (ISI) due to multipath can be effectively rejected using non-linear equalizers, such as Decision Feedback Equalizers (DFEs). [0005] Non-linear equalization techniques, such as Decision Feedback Equalizers, exhibit superior performance when compared on the basis of identical numbers of taps and tap-adaptation algorithms. [0006] The inherent performance advantage of DFEs to combat severe multipath interference makes them attractive for practical channel equalization applications. Nevertheless, DFEs are often used in conjunction with LMS-type algorithms for tap adaptations. As a result, the convergence speed of LMS type or blind equalizers is still dependent on the eigenvalue spread of the input. As an alternative, different techniques have been proposed, such as Recursive Least Squares (RLS), etc. However, implementation complexity often precludes the use of such tap adaptation algorithms in practical applications. [0007] The present invention is therefore directed to the problem of developing a method and apparatus for increasing the convergence speed of a digital channel equalizer without unduly increasing the implementation complexity. [0008] The present invention solves these and other problems by providing an adaptive transform-domain decision feedback equalizer with a convergence speed that is faster than the traditional counterpart at a modest increase in computational complexity. [0009] According to one aspect of the present invention, a method for performing equalization on an input signal in a receiver creates multiple delayed samples of the input signal and orthogonally transforms each of the delayed input samples before weighting them using transformed adaptive coefficients. The weighted orthogonally-transformed delayed input samples are summed along with a feedback signal and the result is output as the equalizer output signal. [0010] According to another aspect of the present invention, the feedback signal is formed from delayed samples of a receiver decision signal, which are orthogonally transformed, then weighted using transformed adaptive coefficients, and finally summed and fed back as the feedback signal. [0011] According to another aspect of the present invention, the feedback signal is formed from delayed samples of a receiver decision signal, which are weighted using adaptive coefficients, and finally summed and fed back as the feedback signal. [0012] An exemplary embodiment of the equalizer herein is particularly suitable for applications with small delay dispersions, such as home networks or LANs. [0013] FIG. 1 depicts a conventional receiver with an equalizer. [0014] FIG. 2 depicts a block diagram of an exemplary embodiment of an apparatus for performing a Transform-Domain Decision Feedback Equalizer (TDDFE) according to one aspect of the present invention. [0015] FIG. 3 depicts a block diagram of an exemplary embodiment of an apparatus for performing a Hybrid DFE (HDFE) according to another aspect of the present invention. [0016] FIG. 4 depicts an exemplary embodiment of a method for computing a transform of a sequence in a recursive manner according to yet another aspect of the present invention. [0017] FIG. 5 depicts a graph of simulation results of the embodiment of FIG. 1 for a paper channel, .mu..sub.1=20, .mu..sub.2=16, LMS (factor 32), averaged over 500 symbols. [0018] It is worthy to note that any reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment. [0019] Turning to FIG. 1, shown therein is an exemplary embodiment of a digital receiver 10 according to one aspect of the present invention. The receiver 10 includes an antenna 11, an analog front end (e.g., a filter, tuner, etc.) 12, and analog-to-digital converter (ADC) 13, a timing/carrier recovery circuit 14, an adaptive equalizer 15 having its own processor 18, a phase-corrector 16 and a receiver decision device (such as a forward error corrector or trellis decoder) 17. 23. [0020] In this exemplary embodiment, the adaptive equalizer (e.g., 20, 30) is also coupled to the receiver decision device (17) and includes a processor (18) to: create delayed versions of the digital signal; orthogonally transform the delayed versions and weight them using transformed adaptive coefficients; sum the weighted and orthogonally-transformed delayed versions of the digital signal along with a feedback signal to create an equalized output signal. Moreover, the processor adaptively updates the transformed adaptive coefficients based on decisions made in the receiver decision device using prior versions of an equalized output signal. This updating is performed in the conventional manner, except that the adaptive coefficients are orthogonally transformed as set forth below. [0021] The present invention concerns the equalization stage of a receiver. The present invention allows decision-feedback equalizers to converge faster than conventional equalizers. Fast convergence is essential in bi-directional packet based digital communications systems, such as wireless Local Area Networks (LANs). Thus, the present invention makes possible receivers that can operate in places with high levels of multipath or that can switch faster between channels/cells. The embodiments herein can be employed in any digital communications system, such as a wireless LAN, which requires channel equalization. [0022] An exemplary embodiment of the present invention provides a transform domain decision feedback equalizer technique. Further, the description herein includes performance evaluations using simulations. The exemplary embodiment exhibits superior performance compared to the traditional LMS type DFEs. From an implementation point of view, this technique is well suited for applications requiring small numbers of taps. [0023] The Transform-Domain DFE, termed herein TDDFE, is based on applying orthogonal transformation of the inputs of both the forward and feedback sections. The orthogonal transform can be a Fast Fourier Transform (FFT), Discrete Cosine Transform (DCT), or another similar transform. The taps of the TDDFE are updated in the inverse-transform domain using orthogonalization techniques. In order to proceed further, we revise the conventional time-domain LMS-DFE relationships: y(n)=x(n)c.sup.T(n)+b(n-1)f.sup.T(n) e(n)=d(n)-y(n) c(n+1)=c(n)+.mu.e(n)x(n)* f(n+1)=f(n)+.mu.e(n)b(n-1)* b(n)=dd[y(n)] (1) where y(n) is the output of the equalizer, x(n)={x(n), x(n+1), . . . , x(n-M+1)} is a vector consisting of the samples of the equalizer input, b(n)={b(n), b(n+1), . . . , b(n-N+1)} is a vector consisting of the input samples b(n) of the feedback section, c(n) is an M-length vector consisting of the coefficients of the feed-forward section of the equalizer, f(n) is an N-length vector consisting of the coefficients of the feedback section of the equalizer, d(n) is a reference signal or a locally generated decision term, e(n) is the error term, .mu. is the adaptation step size, dd[y(n)] is the decision device, `*` denotes complex conjugate and `.sup.T`, denotes transpose operation. We define the orthogonal transform operation in a square matrix format T.sub.1 and T.sub.2 where T.sub.1 is an M.times.M square matrix and T.sub.2 is an N.times.N square matrix. The inverse of these matrices represent the inverse transform, i.e., T.sub.1T.sub.1.sup.-1=T.sub.2T.sub.2.sup.-1=I, where I is the identity matrix. Using this property of the matrices, equation (1) can be described as: y(n)=x(n)T.sub.1T.sub.1.sup.-1c.sup.T(n)+b(n-1)T.sub.2T.sub.2.sup.-1f.sup- .T(n) (2) Defining the transformed variables .chi.(n)=x(n)T.sub.1, .zeta.(n)=c(n)T.sub.1.sup.-1T, .beta.(n)=b(n)T.sub.2, and .nu.(n)=f(n)T.sub.2.sup.-1T, the above equation can be described as: y(n)=.chi.(n).zeta..sup.T(n)+.beta.(n-1).nu..sup.T(n) (3) Equation (3) describes the input output relationship of the TDDFE equalizer where the output is computed using the transformed variables. By multiplying both sides of the tap-adaptation equations in (1) with the transform matrices T.sub.1 and T.sub.2 and considering only the transform operation where T.sub.2=T.sub.2*, we easily find: .zeta.(n+1)=.zeta.(n)+.mu.e(n).chi.*(n) .nu.(n+1)=.nu.(n)+.mu.e(n).beta.*(n) (4) The above equations are just an alternative way of describing the time-domain LMS-type equalizer in the transform domain. As a result, there is no reason to expect that the performance of this equalizer will be different from that of the time-domain counterpart. Nevertheless, these equations provide a simple means by which orthogonalization of the input can be achieved to obtain an equalizer that converges faster and exhibits better tracking behavior. Orthogonalization is achieved by measuring the average power of the transformed inputs and using these in the tap-adaptation equations (4). Defining the average values as: .GAMMA..sub.x(n+1)=.lamda..GAMMA..sub.x(n)+|.chi.(n)|.sup.2 .GAMMA..sub.b(n+1)=.lamda..GAMMA..sub.b(n)+|.beta.(n)|.sup.2 (5) where ||.sup.2 is an element-wise magnitude operator, .lamda. is a positive constant, and .GAMMA..sub.x(n) and .GAMMA..sub.b(n) are the respective average values, the tap-update equations are then modified to: .zeta.(n+1)=.zeta.(n)+.mu.e(n).chi.*(n)/.GAMMA..sub.x(n) .nu.(n+1)=.nu.(n)+.mu.e(n).beta.*(n)/.GAMMA..sub.b(n) (6) where the operation `./` is an element-wise vector division. The gradient terms in (6) consist of almost uncorrelated variables due to the orthogonal transform operation. As a result, each frequency bin is weighted by variables that are not dependent on the other variables. This is similar to having a time-varying adaptation constant for each tap of the equalizer. Since the tap-adaptation is done using uncorrelated variables, it is natural to expect that the convergence speed of this equalizer is relatively insensitive to the eigenvalue spread and that it converges faster than the traditional time-domain LMS equalizer. As pointed out below, this algorithm is in fact an approximate RLS algorithm. The vectors .GAMMA..sub.x and .GAMMA..sub.b are the diagonal elements of the autocorrelation matrix. As a result of this type of RLS type approximation, it shares the behavior of the standard RLS algorithm, but at a reduced computational complexity. [0024] An exemplary embodiment 20 of the top-level architecture of this transform-domain DFE is shown in FIG. 2. The input to the equalizer is fed into N taps 2-1 through 2-N. Each of the outputs from the taps is fed into transform 24. Continue reading about Transform-domain sample-by-sample decision feedback equalizer... 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